If $a + b = -6$ and $x + y + z = -2$, what is $8a - 7x - 7z - 7y + 8b$ ?
Solution: $= 8a + 8b - 7x - 7y - 7z$ $= (8) \cdot (a + b) + (-7) \cdot (x + y + z)$ $= (8) \cdot (-6) + (-7) \cdot (-2)$ $= -48 + 14$ $= -34$